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<p>Atomistic simulations of multi-component systems require accurate descriptions of interatomic interactions to resolve energy differences between competing phases. Particularly challenging are topologically close-packed (TCP) phases with structural similarities and nearly-degenerate different site occupations even in binary systems like Fe–Mo. In this work, data-efficient machine-learning (ML) models are presented that address this challenge by using features with domain knowledge of chemistry and crystallography, enabling accurate and robust predictions for the complex TCP phases <i>R</i>, <i>M</i>, <i>P</i>, and <i>δ</i> with 11–14 WS after training on simple TCP phases <i>A</i>15, <i>σ</i>, <i>χ</i>, <i>μ</i>, <i>C</i>14, <i>C</i>15, and <i>C</i>36 with 2–5 Wyckoff sites (WS). Several ML models based on kernel-ridge regression, multilayer perceptrons, and random forests are trained on fewer than 300 DFT calculations for the simple TCP phases in the Fe–Mo system. Model performance is shown to improve systematically with increasing use of domain knowledge, reaching uncertainties below 25 meV/atom for the predicted convex hulls of the complex TCP phases and showing excellent agreement with DFT verification. Complementary X-ray diffraction experiments and Rietveld analysis are conducted for a Fe–Mo <i>R</i>-phase sample. The measured WS occupancies show excellent agreement with ML-model predictions obtained using the Bragg-Williams approximation at the same temperature.</p>

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Data-efficient machine-learning of complex Fe–Mo intermetallics using domain knowledge of chemistry and crystallography

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月20日

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  • Mariano Forti,
  • Alesya Malakhova,
  • Yury Lysogorskiy,
  • Wenhao Zhang,
  • Jean-Claude Crivello,
  • Jean-Marc Joubert,
  • Ralf Drautz,
  • Thomas Hammerschmidt

摘要

Atomistic simulations of multi-component systems require accurate descriptions of interatomic interactions to resolve energy differences between competing phases. Particularly challenging are topologically close-packed (TCP) phases with structural similarities and nearly-degenerate different site occupations even in binary systems like Fe–Mo. In this work, data-efficient machine-learning (ML) models are presented that address this challenge by using features with domain knowledge of chemistry and crystallography, enabling accurate and robust predictions for the complex TCP phases R, M, P, and δ with 11–14 WS after training on simple TCP phases A15, σ, χ, μ, C14, C15, and C36 with 2–5 Wyckoff sites (WS). Several ML models based on kernel-ridge regression, multilayer perceptrons, and random forests are trained on fewer than 300 DFT calculations for the simple TCP phases in the Fe–Mo system. Model performance is shown to improve systematically with increasing use of domain knowledge, reaching uncertainties below 25 meV/atom for the predicted convex hulls of the complex TCP phases and showing excellent agreement with DFT verification. Complementary X-ray diffraction experiments and Rietveld analysis are conducted for a Fe–Mo R-phase sample. The measured WS occupancies show excellent agreement with ML-model predictions obtained using the Bragg-Williams approximation at the same temperature.